Page 13 - Spring 2007

Fig. 3. Sound intensity distribution in the far-field of a radiating baffled piston, ka=3π.
ton surface). However, at higher frequencies, like koa=3π, the pressure alternates its phase at varying angles. The directivi- ty of the sound radiated by piston sources is usually plotted as a pressure magnitude to remove the effects of alternating phase.
It is hard to generalize how much sound a source makes by considering pressure at a specific location. Therefore, we usually measure or compute the total radiated sound power instead. The total radiated sound power is computed by inte- grating the active acoustic intensity over space.
The active, or propagating acoustic intensity in a fluctu- ating acoustic pressure field is:
(2)
where v􏰀* is the conjugate of the acoustic fluctuating particle velocity. Notice that both the particle velocity and intensity are vector quantities, and point in specific directions. When in the far-field, we consider only the radially propagating component of intensity. Also when in the far-field, the pres- sure and particle velocity are in phase with each other (this is not the case close to the vibrating surface, or in the near- field) and v=p/ροcο. So, in the far-field, the radial component of intensity simplifies to:
(3)
Figure 3 shows the far-field intensity for ka=3π on a dB scale. Notice how all the peak locations are positive, since intensity squares the pressure magnitude. The highest pressure is normal to the piston, with lower amplitude side lobes at var- ious angles. As ka increases, more side lobes will appear.
The total radiated power is computed by integrating the intensity (which is just the localized power/area) over a far- field half-spherical surface surrounding the piston. Spherical surfaces are used to make the integration simple; the total sound power may be integrated over any shaped surface, though.
The radiated sound power is related directly to the radi- ation resistance of the fluid, which acts over the surface of the
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